I've been working (semi-)remotely for the last couple of years. My current schedule has me at home most of the week, and in the office with the rest of the team two days, however that varies depending on other factors.
> How about same-time communication? E.g. I need to discuss things with my designer, oh wait, he's gardening at the moment, or he works at night.
On the whole you avoid it. So much of what people think needs an immediate response really doesn't, and can be dealt with much more effectively with a well written email. If you really do need to speak to someone real time then you schedule a time which is convenient, rather than disrupting the other party by dropping by their desk.
> How do you know when to start/stop your day? E.g. In "normal" office, it's usually 9 to 5.
This was the hardest thing for me when I stopped working in an office, but eventually you get into a rhythm, much as you would in a "normal" job. Sometimes it might vary a bit, but in the end we're creatures of habit.
> How do you schedule projects? Fixed time simplifies scheduling ("This project is 5 man-days").
You still have an idea of how many productive hours you'll get in a typical day, you're just working in a different place. Knowing how much you actually work is a big win for estimation, since you're not playing the game of pretending everyone gets 8 hours a day every day.
> Who pays for supporting equipments (desk, LCD, internet, nice coffee) if I work from home?
In my case, I had it all set up from when I was contracting anyway, so the kit is mine, but it depends on the company. Any company worth their salt would pick up the tab for equipment you need for your job (although you may have to pay for your own coffee).